To demonstrate the robustness of the activity bump control, as well as its different manifestation, we consider the second model: an ensemble of modified bistable spiking oscillators initially discussed in the symmetric form in Refs. [1]}, [2]}, where the resonant stochastic phenomena in the chosen oscillator were demonstrated. In this work, we introduce an asymmetry into the system to achieve the coexistence of a stable limit cycle and a stable steady state. The ensemble under study admits the following form:
\(\begin{array}{rl}\varepsilon \dfrac{dx_{i}}{dt}=&-\left(1+\sqrt{2D}n_{i}(t) \right)y_{i} - a_1 x_{i}\\&+a_3 x_i^3-a_5x_i^5,\\\dfrac{dy_{i}}{dt}=&x_{i}+by_{i}-cy_{i}^2-dy_i^3+\dfrac{\sigma }{2R}\sum \limits ^{i+R}_{j=i-R}(y_j-y_i).\end{array}\) 
